Abstract

Second- and third-order frequency correlations of speckle intensity patterns are used to characterize scattering media for multiple polarization states. The polarized temporal responses thus obtained are sensitive to the degree of scatter, with results being predictable by a diffusion model with sufficiently strong scatter. Experimental data are used to reconstruct various transfer functions.

© 2006 Optical Society of America

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  1. S. R. Arridge, "Optical tomography in medical imaging," Inverse Probl. 15, R41-R93 (1999).
    [CrossRef]
  2. A. B. Milstein, S. Oh, J. S. Reynolds, K. J. Webb, C. A. Bouman, and R. P. Millane, "Three-dimensional Bayesian optical diffusion tomography with experimental data," Opt. Lett. 27, 95-97 (2002).
    [CrossRef]
  3. M. A. O'Leary, D. A. Boas, X. D. Li, B. Chance, and A. G. Yodh, "Fluorescence lifetime imaging in turbid media," Opt. Lett. 21, 158-160 (1996).
    [CrossRef] [PubMed]
  4. A. B. Milstein, S. Oh, K. J. Webb, C. A. Bouman, Q. Zhang, D. A. Boas, and R. P. Millane, "Fluorescence optical diffusion tomography," Appl. Opt. 42, 3081-3094 (2003).
    [CrossRef] [PubMed]
  5. A. B. Milstein, M. D. Kennedy, P. S. Low, C. A. Bouman, and K. J. Webb, "Detection and localization of a fluorescent mouse tumor in a turbid medium," Appl. Opt. 44, 2300-2310 (2005).
    [CrossRef] [PubMed]
  6. J. D. McKinney, M. A. Webster, K. J. Webb, and A. M. Weiner, "Characterization and imaging in optically scattering media by use of laser speckle and a variable-coherence source," Opt. Lett. 25, 4-6 (2000).
    [CrossRef]
  7. S. L. Jacques, J. R. Roman, and K. Lee, "Imaging superficial tissues with polarized light," Lasers Surg. Med. 26, 119-129 (2000).
    [CrossRef] [PubMed]
  8. M. Moscosco, J. B. Keller, and G. Papanicolaou, "Depolarization and blurring of optical images by biological tissue," J. Opt. Soc. Am. A 18, 948-960 (2001).
    [CrossRef]
  9. A. Ishimaru, "Diffusion of light in turbid material," Appl. Opt. 28, 2210-2215 (1989).
    [CrossRef] [PubMed]
  10. K. Furutsu, "Diffusion equation derived from space-time transport equation," J. Opt. Soc. Am. 70, 360-366 (1980).
    [CrossRef]
  11. C. A. Thompson, K. J. Webb, and A. M. Weiner, "Diffusive media characterization using laser speckle," Appl. Opt. 36, 3726-3734 (1997).
    [CrossRef] [PubMed]
  12. D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, "Depolarization of multiply scattered waves by spherical diffusers: Influence of size parameter," Phys. Rev. E 49, 1767-1770 (1994).
    [CrossRef]
  13. F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, "Polarization memory of multiply scattered light," Phys. Rev. B 40, 9342-9345 (1989).
    [CrossRef]
  14. I. Freund, "Optical intensity fluctuations in multiply scattering media," Opt. Commun. 81, 251-258 (1991).
    [CrossRef]
  15. S. M. Cohen, D. Eliyahu, and M. Kaveh, "Vector statistics of multiply scattered waves in random systems," Phys. Rev. A 43, 5748-5751 (1991).
    [CrossRef] [PubMed]
  16. I. I. Tarhan and G. H. Watson, "Polarization microstatistics of laser speckle," Phys. Rev. A 45, 6013-6018 (1992).
    [CrossRef] [PubMed]
  17. P. Bruscaglioni, G. Zaccanti, and Q. Wei, "Transmission of a pulsed polarized light beam through thick, turbid media: numerical results," Appl. Opt. 32, 6142-6150 (1993).
    [CrossRef] [PubMed]
  18. S. G. Demos and R. R. Alfano, "Optical polarization imaging," Appl. Opt. 36, 150-155 (1997).
    [CrossRef] [PubMed]
  19. J. S. Tyo, M. P. Rowe, E. N. Pugh, Jr., and N. Engheta, "Target detection in optically scattering media by polarization-difference imaging," Appl. Opt. 35, 1855-1870 (1996).
    [CrossRef] [PubMed]
  20. J. M. Schmitt, A. H. Gandjbakhche, and R. F. Bonner, "Use of polarized light to discriminate short path photons in a multiple scattering medium," Appl. Opt. 31, 6535-6546 (1992).
    [CrossRef] [PubMed]
  21. S. P. Morgan, M. P. Khong, and M. G. Somekh, "Effects of polarization state and scatterer concentration on optical imaging through scattering media," Appl. Opt. 36, 1560-1565 (1997).
    [CrossRef] [PubMed]
  22. A. H. Hielscher, J. R. Mourant, and I. J. Bigio, "Influence of particle size and concentration on the diffuse backscattering of polarized light from tissue phantoms and biological cell suspensions," Appl. Opt. 36, 125-135 (1997).
    [CrossRef] [PubMed]
  23. A. Z. Genack, "Optical transmission in disordered media," Phys. Rev. Lett. 58, 2043-2046 (1987).
    [CrossRef] [PubMed]
  24. L. G. Shirley and P. A. Lo, "Bispectral analysis of the wavelength dependence of speckle: remote sensing of object shape," J. Opt. Soc. Am. A 11, 1025-1046 (1994).
    [CrossRef]
  25. M. A. Webster, K. J. Webb, A. M. Weiner, J. Y. Xu, and H. Cao, "Temporal response of a random medium from speckle intensity frequency correlations," J. Opt. Soc. Am. A 20, 2057-2070 (2003).
    [CrossRef]
  26. M. A. Webster, T. D. Gerke, A. M. Weiner, and K. J. Webb, "Spectral and temporal speckle field measurements of a random medium," Opt. Lett. 29, 1491-1493 (2004).
    [CrossRef] [PubMed]
  27. T. D. Gerke, M. A. Webster, A. M. Weiner, and K. J. Webb, "Frequency-resolved interferometer measurement of polarized wave propagation in scattering media," J. Opt. Soc. Am. A 22, 2691-2699 (2005).
    [CrossRef]
  28. J. W. Goodman, Statistical Optics (Wiley, 1985).
  29. I. S. Reed, "On a moment theorem for complex Gaussian processes," IRE Trans. Inf. Theory 8, 194-195 (1962).
    [CrossRef]
  30. V. D. Hulst, Light Scattering by Small Particles (Wiley, 1957).
  31. S. Chandrasekhar, Radiative Transfer (Oxford U. Press, 1960).
  32. J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis (Wiley, 1976).
  33. M. Testorf, U. Osterberg, B. Pogue, and K. Paulsen, "Sampling of time- and frequency-domain signals in Monte Carlo simulations of photon migration," Appl. Opt. 38, 236-245 (1999).
    [CrossRef]
  34. X. Wang, L. V. Wang, C. Sun, and C. Yang, "Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
    [CrossRef] [PubMed]
  35. M. Xu, "Electric field Monte Carlo simulation of polarized light propagation in turbid media," Opt. Express 12, 6530-6539 (2004).
    [CrossRef] [PubMed]
  36. T. Aruga and T. Igarashi, "Narrow beam light transfer in small particles: image blurring and depolarization," Appl. Opt. 20, 2698-2705 (1981).
    [CrossRef] [PubMed]
  37. M. S. Patterson, B. Chance, and B. C. Wilson, "Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties," Appl. Opt. 28, 2331-2336 (1989).
    [CrossRef] [PubMed]
  38. C. Brosseau, Fundamentals of Polarized Light: a Statistical Optics Approach (Wiley-Interscience, 1998).
  39. A. Z. Genack and J. M. Drake, "Relationship between optical intensity, fluctuations and pulse propagation in random media," Europhys. Lett. 11, 331-336 (1990).
    [CrossRef]
  40. M. A. Webster, K. J. Webb, and A. M. Weiner, "Temporal response of a random medium from third order laser speckle frequency correlations," Phys. Rev. Lett. 88, 033901 (2002).
    [CrossRef] [PubMed]
  41. A. W. Lohmann and B. Wirnitzer, "Triple correlations," Proc. IEEE 72, 889-901 (1984).
    [CrossRef]
  42. H. Bartelt, A. W. Lohmann, and B. Wirnitzer, "Phase and amplitude recovery from bispectra," Appl. Opt. 23, 3121-3129 (1984).
    [CrossRef] [PubMed]
  43. S. Chandrasekhar, Digital Signal Processing: Spectral Computation and Filter Design (Oxford U. Press, 2001).
  44. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (Wiley, 1996).
  45. E. Kogan and M. Kaveh, "Statistics of fluctuations for two types of crossover: From the ballistic to diffusive regime and from the orthogonal to unitary ensemble," Phys. Rev. B 51, 16400-16402 (1995).
    [CrossRef]
  46. A. A. Chabanov and A. Z. Genack, "Field distributions in the crossover from ballistic to diffusive wave propagation," Phys. Rev. E 56, R1338-R1341 (1997).
    [CrossRef]
  47. A. Garcia-Martin, J. J. Saenz, and M. Nieto-Vesperinas, "Spatial field distributions in the transition from ballistic to diffusive transport in randomly corrugated waveguides," Phys. Rev. Lett. 84, 3578-3581 (2000).
    [CrossRef] [PubMed]
  48. A. Ishimaru, S. Jaruwatanadilok, and Y. Kuga. "Polarized pulse waves in random discrete scatterers," Appl. Opt. 40, 5495-5502 (2001).
    [CrossRef]

2005 (2)

2004 (2)

2003 (3)

2002 (2)

A. B. Milstein, S. Oh, J. S. Reynolds, K. J. Webb, C. A. Bouman, and R. P. Millane, "Three-dimensional Bayesian optical diffusion tomography with experimental data," Opt. Lett. 27, 95-97 (2002).
[CrossRef]

M. A. Webster, K. J. Webb, and A. M. Weiner, "Temporal response of a random medium from third order laser speckle frequency correlations," Phys. Rev. Lett. 88, 033901 (2002).
[CrossRef] [PubMed]

2001 (2)

2000 (3)

A. Garcia-Martin, J. J. Saenz, and M. Nieto-Vesperinas, "Spatial field distributions in the transition from ballistic to diffusive transport in randomly corrugated waveguides," Phys. Rev. Lett. 84, 3578-3581 (2000).
[CrossRef] [PubMed]

J. D. McKinney, M. A. Webster, K. J. Webb, and A. M. Weiner, "Characterization and imaging in optically scattering media by use of laser speckle and a variable-coherence source," Opt. Lett. 25, 4-6 (2000).
[CrossRef]

S. L. Jacques, J. R. Roman, and K. Lee, "Imaging superficial tissues with polarized light," Lasers Surg. Med. 26, 119-129 (2000).
[CrossRef] [PubMed]

1999 (2)

1997 (5)

1996 (2)

1995 (1)

E. Kogan and M. Kaveh, "Statistics of fluctuations for two types of crossover: From the ballistic to diffusive regime and from the orthogonal to unitary ensemble," Phys. Rev. B 51, 16400-16402 (1995).
[CrossRef]

1994 (2)

L. G. Shirley and P. A. Lo, "Bispectral analysis of the wavelength dependence of speckle: remote sensing of object shape," J. Opt. Soc. Am. A 11, 1025-1046 (1994).
[CrossRef]

D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, "Depolarization of multiply scattered waves by spherical diffusers: Influence of size parameter," Phys. Rev. E 49, 1767-1770 (1994).
[CrossRef]

1993 (1)

1992 (2)

1991 (2)

I. Freund, "Optical intensity fluctuations in multiply scattering media," Opt. Commun. 81, 251-258 (1991).
[CrossRef]

S. M. Cohen, D. Eliyahu, and M. Kaveh, "Vector statistics of multiply scattered waves in random systems," Phys. Rev. A 43, 5748-5751 (1991).
[CrossRef] [PubMed]

1990 (1)

A. Z. Genack and J. M. Drake, "Relationship between optical intensity, fluctuations and pulse propagation in random media," Europhys. Lett. 11, 331-336 (1990).
[CrossRef]

1989 (3)

1987 (1)

A. Z. Genack, "Optical transmission in disordered media," Phys. Rev. Lett. 58, 2043-2046 (1987).
[CrossRef] [PubMed]

1984 (2)

1981 (1)

1980 (1)

1962 (1)

I. S. Reed, "On a moment theorem for complex Gaussian processes," IRE Trans. Inf. Theory 8, 194-195 (1962).
[CrossRef]

Alfano, R. R.

Arridge, S. R.

S. R. Arridge, "Optical tomography in medical imaging," Inverse Probl. 15, R41-R93 (1999).
[CrossRef]

Aruga, T.

Bartelt, H.

Bicout, D.

D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, "Depolarization of multiply scattered waves by spherical diffusers: Influence of size parameter," Phys. Rev. E 49, 1767-1770 (1994).
[CrossRef]

Bigio, I. J.

Boas, D. A.

Bonner, R. F.

Bouman, C. A.

Brosseau, C.

D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, "Depolarization of multiply scattered waves by spherical diffusers: Influence of size parameter," Phys. Rev. E 49, 1767-1770 (1994).
[CrossRef]

C. Brosseau, Fundamentals of Polarized Light: a Statistical Optics Approach (Wiley-Interscience, 1998).

Bruscaglioni, P.

Cao, H.

Chabanov, A. A.

A. A. Chabanov and A. Z. Genack, "Field distributions in the crossover from ballistic to diffusive wave propagation," Phys. Rev. E 56, R1338-R1341 (1997).
[CrossRef]

Chance, B.

Chandrasekhar, S.

S. Chandrasekhar, Digital Signal Processing: Spectral Computation and Filter Design (Oxford U. Press, 2001).

S. Chandrasekhar, Radiative Transfer (Oxford U. Press, 1960).

Cohen, S. M.

S. M. Cohen, D. Eliyahu, and M. Kaveh, "Vector statistics of multiply scattered waves in random systems," Phys. Rev. A 43, 5748-5751 (1991).
[CrossRef] [PubMed]

Demos, S. G.

Drake, J. M.

A. Z. Genack and J. M. Drake, "Relationship between optical intensity, fluctuations and pulse propagation in random media," Europhys. Lett. 11, 331-336 (1990).
[CrossRef]

Duderstadt, J. J.

J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis (Wiley, 1976).

Eliyahu, D.

S. M. Cohen, D. Eliyahu, and M. Kaveh, "Vector statistics of multiply scattered waves in random systems," Phys. Rev. A 43, 5748-5751 (1991).
[CrossRef] [PubMed]

Engheta, N.

Freund, I.

I. Freund, "Optical intensity fluctuations in multiply scattering media," Opt. Commun. 81, 251-258 (1991).
[CrossRef]

Furutsu, K.

Gandjbakhche, A. H.

Garcia-Martin, A.

A. Garcia-Martin, J. J. Saenz, and M. Nieto-Vesperinas, "Spatial field distributions in the transition from ballistic to diffusive transport in randomly corrugated waveguides," Phys. Rev. Lett. 84, 3578-3581 (2000).
[CrossRef] [PubMed]

Genack, A. Z.

A. A. Chabanov and A. Z. Genack, "Field distributions in the crossover from ballistic to diffusive wave propagation," Phys. Rev. E 56, R1338-R1341 (1997).
[CrossRef]

A. Z. Genack and J. M. Drake, "Relationship between optical intensity, fluctuations and pulse propagation in random media," Europhys. Lett. 11, 331-336 (1990).
[CrossRef]

A. Z. Genack, "Optical transmission in disordered media," Phys. Rev. Lett. 58, 2043-2046 (1987).
[CrossRef] [PubMed]

Gerke, T. D.

Goodman, J. W.

J. W. Goodman, Statistical Optics (Wiley, 1985).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (Wiley, 1996).

Hamilton, L. J.

J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis (Wiley, 1976).

Hielscher, A. H.

Hulst, V. D.

V. D. Hulst, Light Scattering by Small Particles (Wiley, 1957).

Igarashi, T.

Ishimaru, A.

Jacques, S. L.

S. L. Jacques, J. R. Roman, and K. Lee, "Imaging superficial tissues with polarized light," Lasers Surg. Med. 26, 119-129 (2000).
[CrossRef] [PubMed]

Jaruwatanadilok, S.

Kaveh, M.

E. Kogan and M. Kaveh, "Statistics of fluctuations for two types of crossover: From the ballistic to diffusive regime and from the orthogonal to unitary ensemble," Phys. Rev. B 51, 16400-16402 (1995).
[CrossRef]

S. M. Cohen, D. Eliyahu, and M. Kaveh, "Vector statistics of multiply scattered waves in random systems," Phys. Rev. A 43, 5748-5751 (1991).
[CrossRef] [PubMed]

Keller, J. B.

Kennedy, M. D.

Khong, M. P.

Kogan, E.

E. Kogan and M. Kaveh, "Statistics of fluctuations for two types of crossover: From the ballistic to diffusive regime and from the orthogonal to unitary ensemble," Phys. Rev. B 51, 16400-16402 (1995).
[CrossRef]

Kuga, Y.

Lee, K.

S. L. Jacques, J. R. Roman, and K. Lee, "Imaging superficial tissues with polarized light," Lasers Surg. Med. 26, 119-129 (2000).
[CrossRef] [PubMed]

Li, X. D.

Lo, P. A.

Lohmann, A. W.

Low, P. S.

MacKintosh, F. C.

F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, "Polarization memory of multiply scattered light," Phys. Rev. B 40, 9342-9345 (1989).
[CrossRef]

Martinez, A. S.

D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, "Depolarization of multiply scattered waves by spherical diffusers: Influence of size parameter," Phys. Rev. E 49, 1767-1770 (1994).
[CrossRef]

McKinney, J. D.

Millane, R. P.

Milstein, A. B.

Morgan, S. P.

Moscosco, M.

Mourant, J. R.

Nieto-Vesperinas, M.

A. Garcia-Martin, J. J. Saenz, and M. Nieto-Vesperinas, "Spatial field distributions in the transition from ballistic to diffusive transport in randomly corrugated waveguides," Phys. Rev. Lett. 84, 3578-3581 (2000).
[CrossRef] [PubMed]

Oh, S.

O'Leary, M. A.

Osterberg, U.

Papanicolaou, G.

Patterson, M. S.

Paulsen, K.

Pine, D. J.

F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, "Polarization memory of multiply scattered light," Phys. Rev. B 40, 9342-9345 (1989).
[CrossRef]

Pogue, B.

Pugh, E. N.

Reed, I. S.

I. S. Reed, "On a moment theorem for complex Gaussian processes," IRE Trans. Inf. Theory 8, 194-195 (1962).
[CrossRef]

Reynolds, J. S.

Roman, J. R.

S. L. Jacques, J. R. Roman, and K. Lee, "Imaging superficial tissues with polarized light," Lasers Surg. Med. 26, 119-129 (2000).
[CrossRef] [PubMed]

Rowe, M. P.

Saenz, J. J.

A. Garcia-Martin, J. J. Saenz, and M. Nieto-Vesperinas, "Spatial field distributions in the transition from ballistic to diffusive transport in randomly corrugated waveguides," Phys. Rev. Lett. 84, 3578-3581 (2000).
[CrossRef] [PubMed]

Schmitt, J. M.

D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, "Depolarization of multiply scattered waves by spherical diffusers: Influence of size parameter," Phys. Rev. E 49, 1767-1770 (1994).
[CrossRef]

J. M. Schmitt, A. H. Gandjbakhche, and R. F. Bonner, "Use of polarized light to discriminate short path photons in a multiple scattering medium," Appl. Opt. 31, 6535-6546 (1992).
[CrossRef] [PubMed]

Shirley, L. G.

Somekh, M. G.

Sun, C.

X. Wang, L. V. Wang, C. Sun, and C. Yang, "Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

Tarhan, I. I.

I. I. Tarhan and G. H. Watson, "Polarization microstatistics of laser speckle," Phys. Rev. A 45, 6013-6018 (1992).
[CrossRef] [PubMed]

Testorf, M.

Thompson, C. A.

Tyo, J. S.

Wang, L. V.

X. Wang, L. V. Wang, C. Sun, and C. Yang, "Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

Wang, X.

X. Wang, L. V. Wang, C. Sun, and C. Yang, "Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

Watson, G. H.

I. I. Tarhan and G. H. Watson, "Polarization microstatistics of laser speckle," Phys. Rev. A 45, 6013-6018 (1992).
[CrossRef] [PubMed]

Webb, K. J.

A. B. Milstein, M. D. Kennedy, P. S. Low, C. A. Bouman, and K. J. Webb, "Detection and localization of a fluorescent mouse tumor in a turbid medium," Appl. Opt. 44, 2300-2310 (2005).
[CrossRef] [PubMed]

T. D. Gerke, M. A. Webster, A. M. Weiner, and K. J. Webb, "Frequency-resolved interferometer measurement of polarized wave propagation in scattering media," J. Opt. Soc. Am. A 22, 2691-2699 (2005).
[CrossRef]

M. A. Webster, T. D. Gerke, A. M. Weiner, and K. J. Webb, "Spectral and temporal speckle field measurements of a random medium," Opt. Lett. 29, 1491-1493 (2004).
[CrossRef] [PubMed]

M. A. Webster, K. J. Webb, A. M. Weiner, J. Y. Xu, and H. Cao, "Temporal response of a random medium from speckle intensity frequency correlations," J. Opt. Soc. Am. A 20, 2057-2070 (2003).
[CrossRef]

A. B. Milstein, S. Oh, K. J. Webb, C. A. Bouman, Q. Zhang, D. A. Boas, and R. P. Millane, "Fluorescence optical diffusion tomography," Appl. Opt. 42, 3081-3094 (2003).
[CrossRef] [PubMed]

A. B. Milstein, S. Oh, J. S. Reynolds, K. J. Webb, C. A. Bouman, and R. P. Millane, "Three-dimensional Bayesian optical diffusion tomography with experimental data," Opt. Lett. 27, 95-97 (2002).
[CrossRef]

M. A. Webster, K. J. Webb, and A. M. Weiner, "Temporal response of a random medium from third order laser speckle frequency correlations," Phys. Rev. Lett. 88, 033901 (2002).
[CrossRef] [PubMed]

J. D. McKinney, M. A. Webster, K. J. Webb, and A. M. Weiner, "Characterization and imaging in optically scattering media by use of laser speckle and a variable-coherence source," Opt. Lett. 25, 4-6 (2000).
[CrossRef]

C. A. Thompson, K. J. Webb, and A. M. Weiner, "Diffusive media characterization using laser speckle," Appl. Opt. 36, 3726-3734 (1997).
[CrossRef] [PubMed]

Webster, M. A.

Wei, Q.

Weiner, A. M.

Weitz, D. A.

F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, "Polarization memory of multiply scattered light," Phys. Rev. B 40, 9342-9345 (1989).
[CrossRef]

Wilson, B. C.

Wirnitzer, B.

Xu, J. Y.

Xu, M.

Yang, C.

X. Wang, L. V. Wang, C. Sun, and C. Yang, "Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

Yodh, A. G.

Zaccanti, G.

Zhang, Q.

Zhu, J. X.

F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, "Polarization memory of multiply scattered light," Phys. Rev. B 40, 9342-9345 (1989).
[CrossRef]

Appl. Opt. (15)

A. B. Milstein, S. Oh, K. J. Webb, C. A. Bouman, Q. Zhang, D. A. Boas, and R. P. Millane, "Fluorescence optical diffusion tomography," Appl. Opt. 42, 3081-3094 (2003).
[CrossRef] [PubMed]

A. B. Milstein, M. D. Kennedy, P. S. Low, C. A. Bouman, and K. J. Webb, "Detection and localization of a fluorescent mouse tumor in a turbid medium," Appl. Opt. 44, 2300-2310 (2005).
[CrossRef] [PubMed]

A. Ishimaru, "Diffusion of light in turbid material," Appl. Opt. 28, 2210-2215 (1989).
[CrossRef] [PubMed]

C. A. Thompson, K. J. Webb, and A. M. Weiner, "Diffusive media characterization using laser speckle," Appl. Opt. 36, 3726-3734 (1997).
[CrossRef] [PubMed]

P. Bruscaglioni, G. Zaccanti, and Q. Wei, "Transmission of a pulsed polarized light beam through thick, turbid media: numerical results," Appl. Opt. 32, 6142-6150 (1993).
[CrossRef] [PubMed]

S. G. Demos and R. R. Alfano, "Optical polarization imaging," Appl. Opt. 36, 150-155 (1997).
[CrossRef] [PubMed]

J. S. Tyo, M. P. Rowe, E. N. Pugh, Jr., and N. Engheta, "Target detection in optically scattering media by polarization-difference imaging," Appl. Opt. 35, 1855-1870 (1996).
[CrossRef] [PubMed]

J. M. Schmitt, A. H. Gandjbakhche, and R. F. Bonner, "Use of polarized light to discriminate short path photons in a multiple scattering medium," Appl. Opt. 31, 6535-6546 (1992).
[CrossRef] [PubMed]

S. P. Morgan, M. P. Khong, and M. G. Somekh, "Effects of polarization state and scatterer concentration on optical imaging through scattering media," Appl. Opt. 36, 1560-1565 (1997).
[CrossRef] [PubMed]

A. H. Hielscher, J. R. Mourant, and I. J. Bigio, "Influence of particle size and concentration on the diffuse backscattering of polarized light from tissue phantoms and biological cell suspensions," Appl. Opt. 36, 125-135 (1997).
[CrossRef] [PubMed]

M. Testorf, U. Osterberg, B. Pogue, and K. Paulsen, "Sampling of time- and frequency-domain signals in Monte Carlo simulations of photon migration," Appl. Opt. 38, 236-245 (1999).
[CrossRef]

T. Aruga and T. Igarashi, "Narrow beam light transfer in small particles: image blurring and depolarization," Appl. Opt. 20, 2698-2705 (1981).
[CrossRef] [PubMed]

M. S. Patterson, B. Chance, and B. C. Wilson, "Time resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties," Appl. Opt. 28, 2331-2336 (1989).
[CrossRef] [PubMed]

H. Bartelt, A. W. Lohmann, and B. Wirnitzer, "Phase and amplitude recovery from bispectra," Appl. Opt. 23, 3121-3129 (1984).
[CrossRef] [PubMed]

A. Ishimaru, S. Jaruwatanadilok, and Y. Kuga. "Polarized pulse waves in random discrete scatterers," Appl. Opt. 40, 5495-5502 (2001).
[CrossRef]

Europhys. Lett. (1)

A. Z. Genack and J. M. Drake, "Relationship between optical intensity, fluctuations and pulse propagation in random media," Europhys. Lett. 11, 331-336 (1990).
[CrossRef]

Inverse Probl. (1)

S. R. Arridge, "Optical tomography in medical imaging," Inverse Probl. 15, R41-R93 (1999).
[CrossRef]

IRE Trans. Inf. Theory (1)

I. S. Reed, "On a moment theorem for complex Gaussian processes," IRE Trans. Inf. Theory 8, 194-195 (1962).
[CrossRef]

J. Biomed. Opt. (1)

X. Wang, L. V. Wang, C. Sun, and C. Yang, "Polarized light propagation through scattering media: time-resolved Monte Carlo simulations and experiments," J. Biomed. Opt. 8, 608-617 (2003).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

Lasers Surg. Med. (1)

S. L. Jacques, J. R. Roman, and K. Lee, "Imaging superficial tissues with polarized light," Lasers Surg. Med. 26, 119-129 (2000).
[CrossRef] [PubMed]

Opt. Commun. (1)

I. Freund, "Optical intensity fluctuations in multiply scattering media," Opt. Commun. 81, 251-258 (1991).
[CrossRef]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (2)

S. M. Cohen, D. Eliyahu, and M. Kaveh, "Vector statistics of multiply scattered waves in random systems," Phys. Rev. A 43, 5748-5751 (1991).
[CrossRef] [PubMed]

I. I. Tarhan and G. H. Watson, "Polarization microstatistics of laser speckle," Phys. Rev. A 45, 6013-6018 (1992).
[CrossRef] [PubMed]

Phys. Rev. B (2)

F. C. MacKintosh, J. X. Zhu, D. J. Pine, and D. A. Weitz, "Polarization memory of multiply scattered light," Phys. Rev. B 40, 9342-9345 (1989).
[CrossRef]

E. Kogan and M. Kaveh, "Statistics of fluctuations for two types of crossover: From the ballistic to diffusive regime and from the orthogonal to unitary ensemble," Phys. Rev. B 51, 16400-16402 (1995).
[CrossRef]

Phys. Rev. E (2)

A. A. Chabanov and A. Z. Genack, "Field distributions in the crossover from ballistic to diffusive wave propagation," Phys. Rev. E 56, R1338-R1341 (1997).
[CrossRef]

D. Bicout, C. Brosseau, A. S. Martinez, and J. M. Schmitt, "Depolarization of multiply scattered waves by spherical diffusers: Influence of size parameter," Phys. Rev. E 49, 1767-1770 (1994).
[CrossRef]

Phys. Rev. Lett. (3)

A. Z. Genack, "Optical transmission in disordered media," Phys. Rev. Lett. 58, 2043-2046 (1987).
[CrossRef] [PubMed]

M. A. Webster, K. J. Webb, and A. M. Weiner, "Temporal response of a random medium from third order laser speckle frequency correlations," Phys. Rev. Lett. 88, 033901 (2002).
[CrossRef] [PubMed]

A. Garcia-Martin, J. J. Saenz, and M. Nieto-Vesperinas, "Spatial field distributions in the transition from ballistic to diffusive transport in randomly corrugated waveguides," Phys. Rev. Lett. 84, 3578-3581 (2000).
[CrossRef] [PubMed]

Proc. IEEE (1)

A. W. Lohmann and B. Wirnitzer, "Triple correlations," Proc. IEEE 72, 889-901 (1984).
[CrossRef]

Other (7)

S. Chandrasekhar, Digital Signal Processing: Spectral Computation and Filter Design (Oxford U. Press, 2001).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (Wiley, 1996).

C. Brosseau, Fundamentals of Polarized Light: a Statistical Optics Approach (Wiley-Interscience, 1998).

J. W. Goodman, Statistical Optics (Wiley, 1985).

V. D. Hulst, Light Scattering by Small Particles (Wiley, 1957).

S. Chandrasekhar, Radiative Transfer (Oxford U. Press, 1960).

J. J. Duderstadt and L. J. Hamilton, Nuclear Reactor Analysis (Wiley, 1976).

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Figures (10)

Fig. 1
Fig. 1

Incident field E i propagating along the z axis is scattered by a homogeneous sphere at the origin, and the scattered field E o with a scattering angle θ is shown.

Fig. 2
Fig. 2

Intensity angular distribution for light scattered from a small sphere. In the upper half, the incident field is x-polarized (LP), incident in the z direction ( θ = 0 ) , and the x-, y-, and z-polarized components of the ϕ-integrated scattered light intensity are plotted. The y and z components have a magnification of 3. In the lower half, the incident wave is z-directed RHCP, and RHCP and LHCP components for the scattered light intensity angular distribution are plotted.

Fig. 3
Fig. 3

Experimental setup used to measure the speckle intensity patterns as a function of the laser diode center frequency. The Fabry–Perot interferometer is used to monitor the change in the laser diode center frequency as it is tuned. Lens L1 ( f L 1 = 50 mm ) focuses the laser output onto the front face of the scattering random medium. The spatial structure of the speckle pattern at plane P1 is controlled by the unity magnification spatial filter. Lens L2 ( f L 2 = 75 mm ) provides a magnification factor of M = 10 from the plane P1 to the CCD image plane, where the resultant frequency-dependent speckle pattern is obtained. The combination of polarizer, half-wave plate (HWP) and quarter-wave plate (QWP) before lens L1 is used to control the polarization of the input beam and the polarizer plus QWP after L2 is to select the desired output polarization.

Fig. 4
Fig. 4

(a) Typical intensity speckle pattern from the scattering media studied, captured by a CCD camera, for a 9-mm-thick sample having μ s = 4 cm 1 . The input and output light are both RHCP. (b) Intensity histogram obtained from the speckle pattern given in (a) plotted on a semilogarithmic scale. The negative exponential intensity probability density function fit to the result in (b) is indistinguishable.

Fig. 5
Fig. 5

Measured mean intensity for copolarized and cross-polarized light for LP and CP input as a function of sample thickness, with input power fixed. The sample has μ s = 4 cm 1 .

Fig. 6
Fig. 6

Degree of polarization as a function of sample thickness: linear polarization (crosses), circular polarization (circles). The sample has μ s = 4 cm 1 .

Fig. 7
Fig. 7

Second-order intensity correlations for copolarized and cross-polarized light for scattering samples of various thickness for samples thicknesses of (a) 6 mm , (b) 9 mm , (c) 12 mm , (d) 15 mm , and (e) 18 mm . The triangles show linear polarization and the circles show circular polarization. The solid curves are calculated from a diffusion model using μ s = 4 cm 1 .

Fig. 8
Fig. 8

Reconstructed temporal responses for the 12-mm-thick sample. The inset is a portion of the temporal responses enlarged for clarity. (a) Copolarized light (solid curve) compared with a diffusion model (dashed curve). (b) Cross-polarized light (solid curve) compared with a diffusion model (dashed curve).

Fig. 9
Fig. 9

Reconstructed temporal responses for the 15 mm sample. (a) Copolarized light (solid curve) compared with a diffusion model (dashed curve). (b) Cross-polarized light (solid curve) compared with a diffusion model (dashed curve).

Fig. 10
Fig. 10

Reconstructed temporal responses for the 18 mm sample (solid curve), regardless of polarization, compared with the diffusion model (dashed curve).

Equations (14)

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E o ( ν ) = 1 N k = 1 N A k exp [ j ϕ k ( ν ) ] ,
E ( ν ) = [ x ̂ E x ( ν ) + y ̂ E y ( ν ) ] exp ( j k z ) + c.c. ,
E ( ν ) = [ R ̂ E R ( ν ) + L ̂ E L ( ν ) ] exp ( j k z ) + c.c. ,
t Φ ( r , t ) + v μ a Φ ( r , t ) [ D Φ ( r , t ) ] = v S 0 ( r , t ) ,
J ( r , t ) = D v Φ ( r , t ) .
p D ( t ) = I D ( t ) d t I D ( t ) .
S = ( I Q U V ) = ( E x E x * + E y E y * E x E x * E y E y * E x E y * + E y E x * j ( E x E y * E y E x * ) ) ,
p i j ( t ) = I i j ( t ) d t I i j ( t ) ,
E ( ν + Δ ν ) E * ( ν ) = I P ( Δ ν ) ,
P ( Δ ν ) = d t p ( t ) exp ( j 2 π Δ ν t ) .
I ̃ ( ν + Δ ν ) I ̃ ( ν ) = P ( Δ ν ) 2 ,
I ̃ ( ν ) I ̃ ( ν + Δ ν 1 ) I ̃ ( ν + Δ ν 1 + Δ ν 2 ) = 2 Re { P ( Δ ν 1 ) P ( Δ ν 2 ) P * ( Δ ν 1 + Δ ν 2 ) } .
ψ ( ν 1 , ν 2 ) = ϕ ( ν 1 ) + ϕ ( ν 2 ) ϕ ( ν 1 + ν 2 ) ,
P = I I I + I ,

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